Contrasting carrier doping effects in the Kondo insulator ${\mathrm{CeOs}}_2{\mathrm{Al}}_{10}$: The influential role of $c-f$ hybridization in spin-gap formation

The effects of electron (Ir) and hole (Re) doping on the hybridization gap and antiferromagnetic order have been studied by magnetization, muon spin relaxation $\left({\mu }^{+}\mathrm{SR}\right)$, and inelastic neutron scattering on polycrystalline samples of $\mathrm{Ce}\left({\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x\right){}_2{\mathrm{Al}}_{10}$ $(x=0.08$ and 0.15) and $\mathrm{Ce}\left({\mathrm{Os}}_{1-y}{\mathrm{Re}}_y\right){}_2{\mathrm{Al}}_{10}$ $\left(y=0.03\right)$. ${\mu }^{+}\mathrm{SR}$ spectra clearly reveal bulk magnetic ordering below 20 and 10 K for $x=0.08$ and 0.15 samples, respectively, with heavily damped oscillations of the muon asymmetry. Our important findings are that a small amount of electron doping (i) completely suppresses the inelastic magnetic excitations at low temperatures, which were observed at 11 meV in the undoped compound, and the magnetic response transforms into a broad quasielastic response, and (ii) surprisingly, the internal field at the corresponding muon site is remarkably enhanced by an order of magnitude compared with the parent compound. Moreover, a small amount (3% Re) of hole doping results in a significant reduction of the intensity of 11 meV peak and an increased $c-f$ hybridization, which is in agreement with the reduction of the Ce ordered moment seen through neutron diffraction and ${\mu }^{+}\mathrm{SR}$. The main origin of the observed doping effect is an extra $5d$ electron being carried by Ir and a hole carried by Re with respect to the Os atom. The absence of a spin gap/spin wave, despite a larger ordered state moment of Ce, in the electron-doped system cannot be explained based on a conventional theory of magnetism. Thus, the obtained results demonstrate a great sensitivity to the carrier doping and provide additional ways to study the anomalous magnetic properties in the $\mathrm{Ce}{T}_2{\mathrm{Al}}_{10}$ ($T=$ Fe, Ru, and Os).

Figure 1

(a) Temperature dependence of dc susceptibility $\chi \left(T\right)$ and the inverse $\chi \left(T\right)$ of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ [$x=0$ (inset), 0.08 and 0.15] in an applied magnetic field of 50 kOe. (b) Isothermal field dependence of magnetization at 2 K. Inset: The first derivative of the magnetization with field ($dM/dH$) vs $H$ at 2 K.

Figure 2

(a) Temperature-dependent magnetic susceptibility $\chi \left(T\right)$ of Ce(${\mathrm{Os}}_{1-y}{\mathrm{Re}}_y$)${}_2{\mathrm{Al}}_{10}$ ($y=0.0$, 0.03) in an applied magnetic field of 10 kOe. (b) $M$ vs $H$ isotherms at various temperatures for $y=0.03$.

Figure 3

Zero-field muon spin relaxation spectra at various temperatures of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.08$). The solid lines are least-squares fit to the data as described in the text. Insets: The asymmetry spectra in the short-time region.

Figure 4

The temperature dependence of (a) the initial asymmetries $A_1$, $A_2$, and $A_3$ and (b) the internal field on the muon site. The solid line in (b) is fit to Eq. (3) (see text). (c),(d) The depolarization rates ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ and ${\sigma }_{\mathrm{KT}}$ of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.08$).

Figure 5

Time dependence of muon asymmetry spectra at various temperatures of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.15$). The solid line is a least-squares fit to the data as described in the text. Insets: The spectra in an early-time region.

Figure 6

(a) The initial asymmetries $A_1$, $A_2$, and $A_3$, and (b) the internal field on the muon site. The solid line in (b) is fit to Eq. (3) (see text). (c),(d) The depolarization rates ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ and ${\sigma }_{\mathrm{KT}}$ of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.15$) as a function of temperature.

Figure 7

(a)–(c) The ${\mu }^{+}\mathrm{SR}$ spectra for various applied magnetic fields ($H$ = 0, 50, 100, 250, 500, 1000, 2000, 3000, 4000 and 4500 G) at 30, 15, and 5 K, respectively, for Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.08$).

Figure 8

Inelastic neutron-scattering intensity of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ for (a) $x=0$, (b) $x=0.08$, (c) $x=0.15$, and Ce(${\mathrm{Os}}_{1-y}{\mathrm{Re}}_y$)${}_2{\mathrm{Al}}_{10}$ for (d) $y=0.03$ at 5 K, measured with respective incident energy $E_i=25$ meV on the MARI spectrometer.

Figure 9

$Q$-integrated ($0\le Q\le 2.5$ Å) intensity vs energy transfer of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ for (a) $x=0$, (b) $x=0.08$, (c) $x=0.15$, and Ce(${\mathrm{Os}}_{1-y}{\mathrm{Re}}_y$)${}_2{\mathrm{Al}}_{10}$ for (d) $y=0.03$ along with ${\mathrm{LaOs}}_2{\mathrm{Al}}_{10}$ (red circle) at 5 K, measured with respective incident energy of $E_i=25$ meV. Inset: The INS spectra at 2 K for $x=0.15$.

Figure 10

$Q$-integrated ($0\le Q\le 2.5$ Å) intensity vs energy transfer of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.08$) at 5, 25, 50, and 150 K, respectively, measured with incident energy $E_i=25$ meV. The solid line represents the fit using an inelastic peak (dash-dotted line represents the components of fit), and the dotted line represents a quasielastic peak.

Figure 11

$Q$-integrated ($0\le Q\le 2.5$ Å) intensity vs energy transfer of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.15$) at 5, 30, 50, and 100 K, respectively, measured with incident energy $E_i=25$ meV. The solid line represents the fit using an inelastic peak (dash-dotted line represents the components of fit), and the dotted line represents a quasielastic peak.

Figure 12

(a),(b) The variation of linewidth and susceptibility as a function of temperature obtained from fitting the magnetic scattering intensity of Ce(${\mathrm{Os}}_{1-x}{\mathrm{Ir}}_x$)${}_2{\mathrm{Al}}_{10}$ ($x=0.08$ and 0.15). Lines are guides to the eye.

Figure 13

(a),(b) The $S(Q,\omega )$ for $x=0.0$ (measured with OSIRIS spectrometer) and $x=0.08$ (measured with IRIS spectrometer) at different temperatures, integrated over wave-vector transfer $0.5<Q<1.7$ Å${}^{-1}$.